Electromagnetic coil design is of great importance in many fields of physics and engineering. This is particularly true at the present time in Nuclear Magnetic Resonance (NMR) imaging and spectroscopy, where the requirement for precise spatial variation of a variety of magnetic fields is paramount. The most common arrangement of electromagnetic coil structures for use in NMR is illustrated in FIG. 1 in which an NMR system 1 is shown to comprise a control 2 for operating the system, a main coil 3, usually superconducting, which provides a large, uniform, substantially homogeneous magnetic field over a region of interest (ROI) in the center of the structure, and one axial and two transverse linear gradient field coils 4 (only one being shown for purposes of illustration) that are intended to provide three orthogonal gradient fields that vary linearly over the ROI. The gradient coils shown include an active screen coils 5.
Screen, or shielded gradient coils, and occasionally screened main field coils, have become preferred structures for NMR systems. Active screened coils are described in an article entitled Active Magnetic Screening of Gradient Coils in NMR Imaging by Mansfield et al. J. of Magnetic Resonance 66, p. 573-576 (1986) which discloses a method of systematically screening static or time-dependent stray fields. In this method extraneous magnetic fields outside the active volume of the field gradient coil systems are nulled, while gradient fields of a desired type are intended to be generated in the ROI. Subsequent developments have resulted in integrated coil systems wherein primary gradient coils and screen coils cooperate with one another to produce the gradient magnetic fields in the ROI adjacent to the primary coil structure while creating the external null field. Screened coils are used to permit a field of a specific predetermined type, such as a uniform field, a linear field, or a field having other desired properties to be created within the ROI adjacent to the primary coil structure, while simultaneously producing a substantially zero field adjacent to the screen coil structure.
In FIG. 2, a cylindrical embodiment of portions of an NMR system are shown in which the screen coil 5' and the primary coil 4' are intended to create a given desired or predetermined type of field in the ROI, while providing a null field in which Bz-0 in the region 6 external relative to screen coil 5'. Screened coils are used to eliminate time dependent eddy currents in proximal conducting structures, and hence the resultant time dependent perturbations of the magnetic field in the ROI. It is known that the inductance of screened coils is identical to that of unscreened coils providing the same primary field, since, by definition for screened coils, all flux lines return within the screen such that there is no net flux anywhere. Further, the resistance of the screen coil is also independent of the numbers of arcs (turns) that comprise it. This property results from the fact that the more turns that are present on the screen portion of the structure, the proportionally greater is the amount of current that must be tapped off into a parallel circuit. The reduction in current in the screen is in direct proportion to the increase in the number of turns. Thus if the number of turns is doubled, the current is reduced by half, while the voltage drop, and thus the resistance, remains constant.
Screening also provides a means of greatly reducing the extent of the stray external field from the main coil structure which otherwise has adverse effects on all electronic devices within the local region. Consequently, it is desirable to eliminate, or at least greatly reduce, this external field. The alternative, using passive screening, requires the use of great masses of ferromagnetic material
The significant prior art methods of approaching the general problem of electromagnetic coil design are somewhat arbitrary in their choice of a starting point for the calculation of the surface current distributions of the coils of interest. As a result, the computations tend to be cumbersome and relatively slow, and the resulting coils do not generate optimal fields.
The general problem of electromagnetic coil design is one of solving the Biot-Savart equation set forth below as Equation 1, wherein the quantities B, .mu., and J are vector quantities having three orthogonal spatial components: ##EQU1## where B is the resultant magnetic field at the point r due to the current density distribution J(r') flowing at all points r' within the region of interest, and .mu. is the magnetic permeability of the medium.
Solving the Biot-Savart equation to obtain the magnetic field for a given current distribution, in all but a few very simple cases, has until recently, relied upon numerical integration methods. Solving the reverse problem, that of determining a particular current distribution to produce a desired magnetic field, is more difficult. Frequently, and particularly in the design of electromagnets for NMR, fields are generated by coils wound upon a cylindrical former.
Until recently, solutions of the Biot-Savart equation for such coils were obtained by expanding the magnetic field in terms of spherical harmonics and optimizing the first few non-zero terms at the origin. This method has been in use for over a century and has resulted in the standard Helmholtz and Maxwell coils for uniform and linear axial gradient field designs, respectively. This system generates designs which are essentially a series of line current elements at particular spatial locations.
According to Ampere's law, any theoretically achievable magnetic field can be generated in a region by a corresponding current distribution on a surface enclosing that region. For cylindrical coils, this involves surfaces which are either of infinite length or are closed. For practical reasons, in NMR where access to the space within the coil is essential, the cylinders must be relatively short and open-ended. As a result, the practically achievable magnetic fields, while better than those derived by spherical harmonic expansion, are not perfect, but exhibit distortion from desired field parameters. Therefore, optimization is based on assumptions and compromises which result in undesired distortion of the resultant screen-primary coil generated field in the ROI, or in compromising the null value of the external field, by generating a significant stray field in the null region.
Exact solutions of the Biot-Savart equation of Equation 1, which take into consideration its convoluted nature, were initially derived to solve the problem of eddy current formation in structures external to gradient coils in NMR systems. These solutions have subsequently been applied to the problem of gradient coil design by Turner in 1986 in an article entitled A Target Field Approach to Optimal Coil Design, J. Phys. D:Appl. Phys. 19 (1986) L147-L151, and to integrated shielding gradient coil design in an article by Mansfield et al. entitled Multishield Active Magnetic Screening of Coil Structures in NMR, J. Mag. Resonance 72, 211-223 (1987).. In these latter two cases a suitable (convergent at infinity) "target" field is chosen for the primary gradient field. The choice of such a field is completely arbitrary and does not consider the invariably finite length of the primary coil surface. This results in distortions in the resultant generated field.
In an article by Turner et al., Passive Screening of Switched Magnetic Field Gradients, J. Phys. E. Sci. Instrum. 191 (1986) p. 987-879, a thick cylindrical conductor sleeve is disclosed for passive screening of magnetic field gradients. However, currents induced in such sleeves decay with uncontrolled relaxation times, interfering with the NMR imaging. The decaying current produces image fields superimposed on the desired gradient field, thereby introducing artifacts which can run the image.
An article by Mansfield et al. entitled Active Magnetic Screening of Coils for Static and Time-dependent Magnetic Field Generation in NMR Imaging, J. Phys. E: Sci. Instrum 19 (1986) p. 540-545, discloses a set of current carrying conductors or a discrete wire array used to simulate the induced surface currents which occur in high conductivity thick metal screens placed around coils producing time-dependent fields or field gradients. Strong external fields are made arbitrarily low making it feasible to generate large, rapidly switched gradients within and in close proximity to a superconducting magnet, which is especially useful in NMR imaging. The active screen may comprise a set of conductors or a mesh of equally spaced wires in which a current pattern is externally generated to mimic an induced surface current distribution. An alternative arrangement is one in which the screen wires carry the same current but the wire spacing is unequal. It is disclosed that the field outside the active screen is substantially nulled. However, the problem of obtaining an optimum field in the region of interest (ROI) is not addressed. A disclosure corresponding to these articles appears in British Patent 2,180,943. This patent discloses the active screen as a complete reflector of the magnetic shaped to provide an aperture for access to the volume enclosed by the active screen.
European Patent 0231879 presents an alternative to the above solutions and discloses the optimization of a screen coil by adding terms from a second cylindrical surface. However, the length of the screen coil is a severe constraint. The use of the total available coil length is almost always unsuitable for designing the screen coil parameters. This is because the requisite number of harmonic wavelengths are not necessarily aliquot to this length. As a result, the fields generated by coils of this design exhibit distortion in the presence of the desired null field. A further problem with this approach is that it compromises the null field. Therefore, to eliminate the distortion in the generated field, the null field value is compromised to a non-null value, which can have deleterious effects on the generated field in the ROI.